Can't wire RGB LEDs in series, it would all be parallel per color.
So if you have common anode LEDs, then all anodes would be hooked up to + of your power source.
A resistor from every cathode leg and then join all the cathodes by color. Sink through 3 mosfets.
The reason every LED path gets its own resistor (so 3 resistors per RGB LED), is that when you wire up LEDs in parallel, the variances in actual LED resistances will result in some LEDs passing more current than others, so you will have uneven brightness from one LED to the next. It may be imperceptible, it may be obvious, you may be extremely lucky to have LEDs identical in real-world spec, or most likely some may just burn out from taking the majority of the current due to being the path of least resistance for current.
While not the best way to do it, if this is a cheapie throwaway thing that doesn't really need to definitely last past the holidays, you could only use 1 resistor per color, as long as you recognize that you will likely get uneven coloring and a compromised lifespan of the LEDs.
Not a worthwhile trade-off in my opinion, resistors are a cent per. Do it right.